“We have 4 equations and only 4 unknowns so that gives us a fighting chance of actually solving it.”
— My daughter’s Calculus III teacher
“Of course, he was doing an easy problem compared to the homework. 😛 ”
— My daughter, Niner
Quotations XXVI: On Teaching Math
As I continue to polish the manuscript for my math games book, I’ve been looking for short quotations to put at the beginning of each chapter. I’ve gathered a lot of math quotations over the years, from my own reading and from quote-collection websites. But there’s a problem with using most of these in a book, since to do it right I would have to dig up the original source of each quote and then write a letter to the publisher for permission to use it. And pay a fee that, depending on the publisher’s sense of self-importance, can run into the hundreds of dollars. Bother!
So I went digging around my rss reader to see what sort of inspiration I could find. Bloggers love to be quoted, right? And most of them are happy to give permission via email, which makes my job ever so much easier.
Here are some of the gems I’m considering. I’d love to hear your favorite quotes from math bloggers, too — or favorite passages from your own blog. Please comment!
It’s amazing that this vision of math as “getting to the right answer on your first try” even exists. I have to make, unmake, remake so many mistakes to get where I’m going. I think all mathematicians work that way.
Somehow, a big part of the experience of math is trouble. Frustration is the status quo. But when you get something—the thrill!
Quotable: Math vs. Writing
Seen at kitchen table math, the sequel:
I can recall the deep satisfaction I felt on the all-too-rare occasions at school when the concepts or formulas fell into place. It seemed an entirely different discipline from writing, where something arises from a blank page through a combination of hard work and patience, with a sliver of creativity.
With math, the experience is more like discovering something that’s always existed and finally decided to stop playing hard-to-get.
Still Relevant After All These Years
We have an interesting discussion going in the comments on The Problem with Manipulatives. I mentioned a vague memory of a quotation. Now I’ve found the source.
Originally published in 1970:
The continuing hullabaloo about the “new math” has given many a parent a false impression. What was formerly a dull way of teaching mathematics by rote, so goes the myth, has suddenly been replaced by a marvelous new technique that is achieving miraculous results throughout the nation’s public schools.
I wish it were true — even if only to the extent implied by entertainer (and math teacher) Tom Lehrer in his delightfully whimsical recording on “The New Math”:
“In the new approach, as you know, the important thing is to understand what you’re doing, rather than to get the right answer.”… Indeed, there is something to be said for the old math when taught by a poorly trained teacher. He can, at least, get across the fundamental rules of calculation without too much confusion. The same teacher trying to teach new math is apt to get across nothing at all…
— Martin Gardner
Foreword to Harold Jacobs’ Mathematics: A Human Endeavor
Unfortunately, I can’t embed the Tom Lehrer song Gardner mentioned, due to copyright restrictions, but here’s a link to YouTube:
Quotable: Math is a Game
I don’t love math nearly as much as I pretend I do when I’m teaching it or blogging about it or trying to enthuse my kids.
I just believe — ever since an eye-opening university-level Mathematics in Perspective course — that math is taught VERY badly, bumbled and fumbled and as a result we have this societal fear of what is, essentially, a great big GAME.
See related post — Quotations XXV: Math is a Game
Quotable: What to Do When You’re Stuck
When a kid is feeling bad about being stuck with a problem, or just very anxious, I sometimes ask him to make as many mistakes as he can, and as outrageous as he can. Laughter happens (which is valuable by itself, and not only for the mood — deep breathing brings oxygen to the brain). Then the kid starts making mistakes. In the process, features of the problem become much clearer, and in many cases a way to a solution presents itself.
— Maria Droujkova
Natural Math discussion of math club activities
Does It Work?
While I was collecting entries for the Math Teachers at Play #35 blog carnival, I ran across this post by Dave Lanovaz:
Quotable: Math Programs
Recognize that every math program, whether more traditionally skill-based or reform-oriented (more problem-solving, projects, less drill) has its merits and its weaknesses. Whether you believe there is too much emphasis on basic facts (less likely!), or not enough, you can supplement with the myriad of resources on the web.
— David Marain, MathNotations
Odds and Evens Week of 12-1-10
Click through to the original post for a counting puzzle, plenty of advice on helping with your child’s math homework, useful math links, and a couple of “cute 3-year-old” stories.
And remember that one of the best ways to supplement any math program is by playing games.
Quotations XXV: Math is a Game
Mathematics is a game played according to certain simple rules with meaningless marks on paper.
— David Hilbert
quoted by Nicholas Rose, Mathematical Maxims and MinimsIt’s like asking why Beethoven’s Ninth symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.
Quotable: Times Tables Are Not Math
Important note: times tables are not math. Math doesn’t need to be made fun; it already is fun. Memorizing your times tables is a rote activity, it requires a fair bit of repetition for most, and it may need to be made fun. Just saying.
— Dan Finkel
A game to end all times tables drills: Damult Dice
It’s a great game! Do click over to Dan’s blog and check it out:
And while we’re on the topic of times tables, Maria posted an article, too:
Quotable: Bad at Math
There’s a tendency for adults to label the math that they can do (such as identifying patterns, choosing between competing offers in a supermarket, and challenging statistics published by the government) as “common sense” and labeling everything they can’t do as “math” — so that being bad at math becomes a self-fulfilling prophecy.
— Rob Eastaway, Mike Askew
Old Dogs, New Math: Homework Help for Puzzled Parents
Still a couple of slots left in Sol’s book giveaway. I’ll be hosting a giveaway soon, too — so watch this spot!
Denise Gaskins' Let's Play Math 